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   <h4 class="subsectionHead"><span class="titlemark">2.11   </span> <a 
 id="x16-580002.11"></a>XFEM elements</h4>
<!--l. 1384--><p class="noindent" >XFEM elements allow simulations where the unknown fields are enriched through the partition of unity concept. Two
elements are currently available for 2D XFEM simulations: <span 
class="cmti-10">TrPlaneStress2dXFEM </span>(subclass of <span 
class="cmti-10">TrPlaneStress2d</span>) and
<span 
class="cmti-10">PlaneStress2dXfem </span>(subclass of PlaneStress2d).
<!--l. 1389--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">2.11.1   </span> <a 
 id="x16-590002.11.1"></a>TrPlaneStress2dXFEM element</h5>
<div class="center" 
>
<!--l. 1394--><p class="noindent" >
<div class="table">
<!--l. 1394--><p class="noindent" ><a 
 id="x16-5900144"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-45" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-45-1g"><col 
id="TBL-45-1"></colgroup><colgroup id="TBL-45-2g"><col 
id="TBL-45-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-45-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-45-1-2"  
class="td11"><!--l. 1394--><p class="noindent" ><span 
class="cmbx-10">TrPlaneStress2dXFEM</span>                                    </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-2-2"  
class="td11"><!--l. 1394--><p class="noindent" >Two dimensional 3-node triangular XFEM element          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-45-3-2"  
class="td11"><!--l. 1394--><p class="noindent" >[<span 
class="cmtt-10">czmaterial</span>&#x00A0;#<span 
class="cmr-5">(in)</span>] [<span 
class="cmtt-10">nipcz</span>&#x00A0;#<span 
class="cmr-5">(in)</span>][<span 
class="cmtt-10">useplanestrain</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]   </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-45-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-4-2"  
class="td11"><!--l. 1395--><p class="noindent" ><span 
class="cmtt-10">czmaterial</span>: Interface material for the cohesive zone. (If
no  material  is  specified,  traction  free  crack  surfaces  are
assumed.)                                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-5-1"  
class="td11">                </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-5-2"  
class="td11"><!--l. 1397--><p class="noindent" ><span 
class="cmtt-10">nipcz</span>: Number of integration points used on each segment
of the cohesive zone.                                                  </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-6-1"  
class="td11">                </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-6-2"  
class="td11"><!--l. 1399--><p class="noindent" ><span 
class="cmtt-10">useplanestrain</span>: If plane strain or plane stress should be
assumed. 0 implies plane stress and 1 implies plane strain.</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-7-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-7-2"  
class="td11"><!--l. 1403--><p class="noindent" >Two            continuous            (standard)            DOFs
(u-displacement, v-displacement) and a variable number of
enriched DOFs (can be continuous or discontinuous).       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-8-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-8-2"  
class="td11"><!--l. 1404--><p class="noindent" >-                                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-9-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-9-2"  
class="td11"><!--l. 1406--><p class="noindent" >Elements  cut  by  an  XFEM  interface  are  divided  into
subtriangles.                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-10-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-10-2"  
class="td11"><!--l. 1407--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-45-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-11-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-45-11-2"  
class="td11"><!--l. 1408--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-12-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-12-2"  
class="td11"><!--l. 1409--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-45-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-13-1"  
class="td11">Nlgeo </td> <td  style="white-space:wrap; text-align:left;" id="TBL-45-13-2"  
class="td11"><!--l. 1410--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-14-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-14-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-14-2"  
class="td11"><!--l. 1411--><p class="noindent" >-                                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-15-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-15-1"  
class="td11">Note                   </td><td  style="white-space:wrap; text-align:left;" id="TBL-45-15-2"  
class="td11"><!--l. 1412--><p class="noindent" >Test case: sm/xFemCrackVal.in                                   </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-45-16-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-16-1"  
class="td11">                </td></tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-45-17-"><td  style="white-space:nowrap; text-align:left;" id="TBL-45-17-1"  
class="td11"></td></tr></table>
</div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;44: </span><span  
class="content">TrPlaneStress2dXFEM element summary</span></div><!--tex4ht:label?: x16-5900144 -->
</div><hr class="endfloat" />
</div>
</div>
<!--l. 1416--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">2.11.2   </span> <a 
 id="x16-600002.11.2"></a>PlaneStress2dXfem element</h5>
<div class="center" 
>
<!--l. 1421--><p class="noindent" >
<div class="table">
                                                                                           
                                                                                           
<!--l. 1421--><p class="noindent" ><a 
 id="x16-6000145"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-46" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-46-1g"><col 
id="TBL-46-1"></colgroup><colgroup id="TBL-46-2g"><col 
id="TBL-46-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-46-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-46-1-2"  
class="td11"><!--l. 1421--><p class="noindent" ><span 
class="cmbx-10">PlaneStress2dXfem</span>                                         </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-2-2"  
class="td11"><!--l. 1421--><p class="noindent" >Two dimensional 4-node quad XFEM element                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-46-3-2"  
class="td11"><!--l. 1421--><p class="noindent" >[<span 
class="cmtt-10">czmaterial</span>&#x00A0;#<span 
class="cmr-5">(in)</span>] [<span 
class="cmtt-10">nipcz</span>&#x00A0;#<span 
class="cmr-5">(in)</span>][<span 
class="cmtt-10">useplanestrain</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]   </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-46-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-4-2"  
class="td11"><!--l. 1422--><p class="noindent" ><span 
class="cmtt-10">czmaterial</span>: Interface material for the cohesive zone. (If
no  material  is  specified,  traction  free  crack  surfaces  are
assumed.)                                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-5-1"  
class="td11">                </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-5-2"  
class="td11"><!--l. 1424--><p class="noindent" ><span 
class="cmtt-10">nipcz</span>: Number of integration points used on each segment
of the cohesive zone.                                                  </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-6-1"  
class="td11">                </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-6-2"  
class="td11"><!--l. 1426--><p class="noindent" ><span 
class="cmtt-10">useplanestrain</span>: If plane strain or plane stress should be
assumed. 0 implies plane stress and 1 implies plane strain.</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-7-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-7-2"  
class="td11"><!--l. 1430--><p class="noindent" >Two            continuous            (standard)            DOFs
(u-displacement, v-displacement) and a variable number of
enriched DOFs (can be continuous or discontinuous).       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-8-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-8-2"  
class="td11"><!--l. 1431--><p class="noindent" >-                                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-9-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-9-2"  
class="td11"><!--l. 1433--><p class="noindent" >Elements  cut  by  an  XFEM  interface  are  divided  into
subtriangles.                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-10-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-10-2"  
class="td11"><!--l. 1434--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-46-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-11-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-46-11-2"  
class="td11"><!--l. 1435--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-12-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-12-2"  
class="td11"><!--l. 1436--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-46-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-13-1"  
class="td11">Nlgeo </td> <td  style="white-space:wrap; text-align:left;" id="TBL-46-13-2"  
class="td11"><!--l. 1437--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-14-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-14-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-14-2"  
class="td11"><!--l. 1438--><p class="noindent" >-                                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-15-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-15-1"  
class="td11">Note                   </td><td  style="white-space:wrap; text-align:left;" id="TBL-46-15-2"  
class="td11"><!--l. 1440--><p class="noindent" >Test             cases:             sm/xFemCrackValBranch.in,
sm/xfemCohesiveZone1.in, benchmark/xfem01.in            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-46-16-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-16-1"  
class="td11">                </td></tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-46-17-"><td  style="white-space:nowrap; text-align:left;" id="TBL-46-17-1"  
class="td11"></td></tr></table>
</div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;45: </span><span  
class="content">PlaneStress2dXfem element summary</span></div><!--tex4ht:label?: x16-6000145 -->
</div><hr class="endfloat" />
</div>
</div>
                                                                                           
                                                                                           
                                                                                           
                                                                                           
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